Optimal-Point Variance Reduction For Bayesian Optimization With Regret Guarantee
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866913176683020288 |
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| author | Takeno, Shion |
| author_facet | Takeno, Shion |
| contents | This paper studies a one-step lookahead Bayesian optimization (BO) method and its theoretical guarantee. Although the empirical effectiveness of one-step lookahead BO methods, such as entropy search, has been studied extensively, they often rely on computationally intractable approximations, and their regret guarantees remain underdeveloped. Thus, this paper proposes a one-step lookahead BO method called optimal-point variance reduction (OVR), which requires only posterior sampling and Monte Carlo approximations. We obtain a uniform error bound over an input domain for the Monte Carlo estimation in OVR. Furthermore, we show that the regularized OVR, with the slight modification to promote exploration, achieves a vanishing Bayesian expected simple regret upper bound. Finally, we demonstrate the effectiveness of OVR through numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_00956 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimal-Point Variance Reduction For Bayesian Optimization With Regret Guarantee Takeno, Shion Machine Learning This paper studies a one-step lookahead Bayesian optimization (BO) method and its theoretical guarantee. Although the empirical effectiveness of one-step lookahead BO methods, such as entropy search, has been studied extensively, they often rely on computationally intractable approximations, and their regret guarantees remain underdeveloped. Thus, this paper proposes a one-step lookahead BO method called optimal-point variance reduction (OVR), which requires only posterior sampling and Monte Carlo approximations. We obtain a uniform error bound over an input domain for the Monte Carlo estimation in OVR. Furthermore, we show that the regularized OVR, with the slight modification to promote exploration, achieves a vanishing Bayesian expected simple regret upper bound. Finally, we demonstrate the effectiveness of OVR through numerical experiments. |
| title | Optimal-Point Variance Reduction For Bayesian Optimization With Regret Guarantee |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2606.00956 |